Distributed acoustic sensing using multi-band time-gated digital orthogonal frequency domain reflectometry

ABSTRACT

Aspects of the present disclosure describe systems, methods, and structures for distributed acoustic sensing using multi-band time-gated digital orthogonal frequency domain reflectometry.

CROSS REFERENCE

This disclosure claims the benefit of U.S. Provisional PatentApplication Ser. No. 63/027,527 filed May 20, 2020 the entire contentsof which is incorporated by reference as if set forth at length herein.

TECHNICAL FIELD

This disclosure relates generally to distributed fiber optic sensing(DFOS). More particularly it pertains to DFOS/distributed acousticsensing (DAS) systems, methods, and structures employing multi-bandtime-gated digital orthogonal frequency domain reflectometry.

BACKGROUND

As is known in the art, time-gated digital optical frequency-domainreflectometry (TGD-OFDR) is a coding technique that can be used toincrease signal-to-noise ratio (SNR) in distributed acoustic sensingsystems and methods by signal correlation. Given the importance of DASsystems and methods in a great number of important contemporaryindustrial and societal applications, improvements to such systems andmethods would represent a welcome addition to the art.

SUMMARY

An advance in the art is made according to aspects of the presentdisclosure directed to systems, methods, and structures for distributedacoustic sensing distributed acoustic sensing employing multi-bandtime-gated digital orthogonal frequency domain reflectometry.

In sharp contrast to the prior art, systems, methods, and structuresaccording to aspects of the present disclosure provide distributedacoustic sensing use chirped optical pulses of selectable duration andbandwidth, at a frame rate limited by a round-trip propagation time of afiber under test. And, instead of processing a transmitted chirped pulseas a single sequence—our inventive systems, methods, and structuresemploy a parallel fragmented multiband architecture, where eachtributary correlates the received signal with a truncated chirped pulseto obtain the Rayleigh impulse response over its frequency band. Byreducing the duration of the chirp processed by each tributary, spatialleakage is reduced at all the tributaries, thus even after combining allthe interferometric products from all tributaries using a rotated vectorsum, the resultant signal is much less impacted by spatial leakage thanby using the conventional TGD-OFDR method.

Of further advantage, our digital signal processing (DSP) architectureis also quite flexible, as the number of fragmented tributaries used atthe receiver is independent of the chirped pulse generator—i.e., thegenerator can always transmit the same signal, and the receiverdetermines how to process Rayleigh backscatter considering a trade-offbetween good spatial resolution and low spatial leakage.

BRIEF DESCRIPTION OF THE DRAWING

A more complete understanding of the present disclosure may be realizedby reference to the accompanying drawing in which:

FIG. 1 shows a schematic diagram of an illustrative architecturalarrangement of a correlation-based DAS interrogator including agenerator that launches chirped pulses into a fiber under test (FUT),and detects by a coherent receiver Rayleigh backscatter, according toaspects of the present disclosure;

FIG. 2 shows a schematic diagram of an illustrative experimental setupto demonstrate spatial leakage in a correlation-based DAS usingdifferent correlation codes wherein a piezoelectric transducer (PZT) isinterposed between a 50 km and 25 km spool of single mode fiber,according to aspects of the present disclosure;

FIG. 3(A) and FIG. 3(B) are plots showing DAS results obtained inTGD-OFDR experiments showing the impact of spatial leakage in which:FIG. 3(A) shows measured vibration spectrum versus distance; and FIG.3(B) shows vibration power vs distance at 110 Hz, according to aspectsof the present disclosure;

FIG. 4(A) and FIG. 4(B) are schematic illustrations showing thepartitioning of a long chirp sequence of duration T_(c) and bandwidthαT_(c) into N_(b) shorter chirp sequences, each of duration αT_(c)/N_(b)and duration T_(c)/N_(b) wherein FIG. 4(A) shows a time-domainrepresentation of a real part of x(t)=√{square root over(P)}exp(j2πα(t²/2)) for −T_(c)/2≤t<+T_(c)/2, and FIG. 4(B) shows aninstantaneous frequency of x(t), i.e., f(t)=αt for −T_(c)/2≤t<+T_(c)/2;

FIG. 5(A) and FIG. 5(B) are plots showing instantaneous frequencyprofile f(t) for: FIG. 5(A) TGD-OFDR frame; and FIG. 5(B) MB-DF-OFDRframe according to aspects of the present disclosure;

FIG. 6 shows a schematic diagram of an illustrative DSP architecture forMB-DF-OFDR according to aspects of the present disclosure; and

FIG. 7(A) and FIG. 7(B) are plots showing DAS output obtained in afive-band MP-DF-OFDR experiment, showing improvement over TGD-OFDRwherein: FIG. 7(A) is of measured vibration spectrum versus distance;and FIG. 7(B) is of vibration power vs distance at 110 Hz, according toaspects of the present disclosure.

The illustrative embodiments are described more fully by the Figures anddetailed description. Embodiments according to this disclosure may,however, be embodied in various forms and are not limited to specific orillustrative embodiments described in the drawing and detaileddescription.

DESCRIPTION

The following merely illustrates the principles of the disclosure. Itwill thus be appreciated that those skilled in the art will be able todevise various arrangements which, although not explicitly described orshown herein, embody the principles of the disclosure and are includedwithin its spirit and scope.

Furthermore, all examples and conditional language recited herein areintended to be only for pedagogical purposes to aid the reader inunderstanding the principles of the disclosure and the conceptscontributed by the inventor(s) to furthering the art and are to beconstrued as being without limitation to such specifically recitedexamples and conditions.

Moreover, all statements herein reciting principles, aspects, andembodiments of the disclosure, as well as specific examples thereof, areintended to encompass both structural and functional equivalentsthereof. Additionally, it is intended that such equivalents include bothcurrently known equivalents as well as equivalents developed in thefuture, i.e., any elements developed that perform the same function,regardless of structure.

Thus, for example, it will be appreciated by those skilled in the artthat any block diagrams herein represent conceptual views ofillustrative circuitry embodying the principles of the disclosure.

Unless otherwise explicitly specified herein, the FIGs comprising thedrawing are not drawn to scale.

By way of some additional background we begin by noting that distributedfiber optic sensing (DFOS) is an important and widely used technology todetect environmental conditions such as temperature (distributedtemperature sensing—DTS), vibration (distributed vibration sensing—DVS),stretch level etc. anywhere along an optical fiber cable that in turn isconnected to an interrogator. As is known, contemporary interrogatorsare systems that generate an input signal to the fiber anddetects/analyzes the reflected/scattered and subsequently receivedsignal(s). The signals are analyzed, and an output is generated which isindicative of the environmental conditions encountered along the lengthof the fiber. The signal(s) so received may result from reflections inthe fiber, such as Raman backscattering, Rayleigh backscattering, andBrillion backscattering. It can also be a signal of forward directionthat uses the speed difference of multiple modes. Without losinggenerality, the following description assumes reflected signal thoughthe same approaches can be applied to forwarded signal as well.

As will be appreciated, a contemporary DFOS system includes aninterrogator that periodically generates optical pulses (or any codedsignal) and injects them into an optical fiber. The injected opticalpulse signal is conveyed along the optical fiber.

At locations along the length of the fiber, a small portion of signal isreflected and conveyed back to the interrogator. The reflected signalcarries information the interrogator uses to detect—forexample—vibrations occurring at one or more points along the length ofthe fiber.

Those skilled in the art will understand and appreciate that time-gateddigital optical frequency-domain reflectometry (TGD-OFDR) is one ofcoding technique that can be used to increase signal-to-noise ratio(SNR) in distributed acoustic sensing (DAS) by signal correlation. Byinterrogating an optical fiber-under-test (FUT) with chirped pulses:

$\begin{matrix}{{x(t)} = {\sqrt{P}{\exp\left( {j\; 2\;{\pi\alpha}\frac{t^{2}}{2}} \right)}{{rect}\left( \frac{t}{T_{c}} \right)}}} & (1)\end{matrix}$

where T_(c) is the chirp duration, α is the chirp rate, and √{squareroot over (P)} is the amplitude of the envelope, the total energylaunched into the fiber per interrogation is ε=P·T_(c), while bandwidthof the interrogation signal x(t) is B_(W)=αT_(c).

Compared with optical time-domain reflectometry (OTDR) at the same peakpower (which is limited by fiber nonlinearity) and bandwidth, but whichuses pulses

${p(t)} = {\sqrt{P}{{rect}\left( \frac{t}{T} \right)}}$

of duration T and bandwidth B_(W)=1/T, the energy of the interrogationsignal in TGD-OFDR is

$\frac{T_{c}}{T} = \frac{1}{\alpha\; T^{2}}$

times higher than OTDR. Hence, the power of the received Rayleighbackscatter and SNR also scales accordingly as T_(c)=1/αT.

FIG. 1 shows a schematic diagram of an illustrative architecturalarrangement of a correlation-based DAS interrogator including agenerator that launches chirped pulses into a fiber under test (FUT),and detects by a coherent receiver Rayleigh backscatter, according toaspects of the present disclosure.

Consider the canonical architecture of a correlation-based DAS shown inFIG. 1 where a dual-polarization coherent receiver is used to detect theRayleigh backscatter. When TGD-OFDR is applied in the absence of anyphase modulation by laser phase noise or mechanical vibration of theFUT, received signal is:

$\begin{matrix}{{y(t)} = {{\int\limits_{0}^{L}{{h(z)}{x\left( {t - \frac{2z}{v_{g}}} \right)}{dz}}} + {n(t)}}} & (2)\end{matrix}$

where h(z)=[h_(x)(z) h_(y)(z)]^(T) is the Jones' vector for the Rayleighimpulse response, n(t) is the equivalent additive white Gaussian noise(AWGN) added by the receiver and by any inline amplifiers along the FUT,and v_(g) the group velocity of the fiber at the wavelength λ of thesensing channel. By letting t′=2z/v_(g), Eq. (2) may be recast as alinear convolution:

$\begin{matrix}{{y(t)} = {{\int\limits_{0}^{T_{L}}{{g\left( t^{\prime} \right)}{x\left( {t - t^{\prime}} \right)}{dt}^{\prime}}} = {{{g(t)} \otimes {x(t)}} + {n(t)}}}} & (3)\end{matrix}$

where

${g(t)} = {\frac{v_{g}}{2}{h\left( {\frac{v_{g}}{2}t} \right)}}$

is the Rayleigh impulse response in time-domain, and T_(L)=2n_(eff)L/cis the round-trip propagation time of the FUT.

The Rayleigh impulse response may be estimated by correlating the y(t)with the complex conjugate of the TGD-OFDR signal:

ĝ(t)=x*(t)*y(t)=x*(−t)⊗y(t).  (4)

This operation relies on the good autocorrelation property of chirpedpulses:

R _(xx)(t)=x*(t)*x(t)=(T _(c) −|t|)sinc(αt(T _(c) −|t|)),  (5)

For long chirps T_(c)«T, Eq. (5) has a main lobe with durationT=1/αT_(c), which is the same width as the rectangular pulse used inOTDR. We have:

$\begin{matrix}{{{R_{xx}(t)} \approx {T_{c}{{sinc}\left( \frac{t}{T} \right)}}},} & (6)\end{matrix}$

The correlation output of Eq. (3) is thus approximately equal to thetime-domain Rayleigh impulse response g(t) filtered between frequencies±½T, multiplied by a gain of T_(c). Thus, it appears as if the SNRperformance of TGD-OFDR can be improved linearly without limit byincreasing the chirp duration T_(c), due to increased energy launchedinto the FUT.

In practice, however, the use of very long chirp duration is susceptibleto distortion by phase modulation on both the outbound interrogationsignal as well as the inbound Rayleigh backscatter. Consider first theimpact of vibration of the FUT on outbound signal.

Let ϵ(z; t) denote the longitudinal fiber strain at position z and timet. When the outbound signal reaches z, it is given by:

$\begin{matrix}{{x_{z}(t)} = {{x\left( {t - \frac{z}{v_{g}}} \right)}{\exp\left( {{- j}k{\int\limits_{0}^{z}{{\epsilon\left( {z^{\prime};{t - \frac{z}{v_{g}} + \frac{z^{\prime}}{v_{g}}}} \right)}{dz}^{\prime}}}} \right)}}} & (7)\end{matrix}$

where k=2πn_(eff)/λ is the propagation constant, and n_(eff) is thefiber's effective index of refraction at the wavelength of the sensingchannel.

We observe that the original signal x(t) has been phase-modulated byaccumulated longitudinal strain. The Rayleigh reflection of amplitudeh(z) at position z will contribute a reflected signal of:

$\begin{matrix}{{y_{z}(t)} = {{\left\{ {{h(z)} \cdot {x_{z}\left( {t - \frac{z}{v_{g}}} \right)}} \right\}{\exp\left( {{- j}k{\int\limits_{0}^{z}{{\epsilon\left( {z^{\prime};{t - \frac{z^{\prime}}{v_{g}}}} \right)}{dz}^{\prime}}}} \right)}} = {\left\{ {{h(z)} \cdot \left\lbrack {{x\left( {t - \frac{2z}{v_{g}}} \right)}{\exp\left( {{- j}k{\int_{0}^{z}{{\epsilon\left( {z^{\prime};{t - \frac{2z}{v_{g}} + \frac{z^{\prime}}{v_{g}}}} \right)}{dz}^{\prime}}}} \right)}} \right\rbrack} \right\}{{\exp\left( {{- j}k{\int_{0}^{z}{{\epsilon\left( {z^{\prime};{t - \frac{z^{\prime}}{v_{g}}}} \right)}{dz}^{\prime}}}} \right)}.}}}} & (8)\end{matrix}$

The total received signal (ignoring noise contributions) can be found bysumming all the infinitesimal reflections y_(z)(t):

$\begin{matrix}{{y(t)} = {{\int\limits_{0}^{L}{{y_{z}(t)}{dz}}} = {\int\limits_{0}^{T_{L}}{{{g\left( t^{\prime} \right)} \cdot \left\lbrack {{x\left( {t - t^{\prime}} \right)}{\exp\left( {{- {jk}}{\underset{0}{\int\limits^{\frac{v_{g}t^{\prime}}{2}}}{{\epsilon\left( {z^{\prime};{t - t^{\prime} + \frac{z^{\prime}}{v_{g}}}} \right)}{dz}^{\prime}}}} \right)}} \right\rbrack}{\exp\left( {{- {jk}}{\underset{0}{\int\limits^{\frac{v_{g}t^{\prime}}{2}}}{{\epsilon\left( {z^{\prime};{t - \frac{z^{\prime}}{v_{g}}}} \right)}{dz}^{\prime}}}} \right)}{dt}^{\prime}}}}} & (9)\end{matrix}$

Compared with the simple convolution in Eq. (3), the received signal inEq. (9) is distorted by two phase modulations on the both the outboundsignal and the inbound Rayleigh backscatter due to time-varyinglongitudinal strain. The result is that correlation by x*(t) in Eq. (3)will produce a distorted ĝ(t), as the sinc(·) autocorrelation propertyof in Eq. (6) no longer holds.

The impact of phase distortion on DAS is “spatial leakage,” wherevibration at z_(v) will leak to fiber positions z>z_(v).

FIG. 2 shows a schematic diagram of an illustrative experimental setupto demonstrate spatial leakage in a correlation-based DAS usingdifferent correlation codes wherein a piezoelectric transducer (PZT) isinterposed between a 50 km and 25 km spool of single mode fiber,according to aspects of the present disclosure.

We illustrate spatial leakage with an example from a DAS experimentconducted on a FUT where a piezoelectric transducer (PZT) is insertedbetween two spools of 50-km and 25-km standard single-mode fiber (SSFM)as shown in that FIG. 2. The experiment used a chirped pulse of durationof T_(c)=50 μs and a chirp width 1/T=10 MHz (spatial resolutionΔz=(c/2n_(eff))T≈10 m).

The PZT includes of 12 m of fiber wound on a piezoelectric ring, and hasa slope of 0.8 rad/V. In this experiment, the PZT was driven with a sinewave of 10 V amplitude (phase amplitude Φ₀≈8 rad) at a frequency off_(vib)=110 Hz. The DAS interrogator launched chirped pulses at a framerate of 1,000 Hz.

FIG. 3(A) shows a frequency spectrum vs distance plot for thedifferential beat product ˜ĝ(t)ĝ*(t−Δt_(g)) where a gauge length ofΔz_(g)=(v_(g)/2)Δt_(g)=20 m was used. Since the DAS samples distributedvibration at a frame rate of 1/T_(f)=1, 000 Hz, higher-order harmonicsof exp(jΦ₀ cos(2πf_(vib)t+θ)) are aliased around the Nyquist frequencyof ½T_(f)=500 Hz. It is observed that the 110 Hz vibration is not merelyconfined to the location of the PZT (z=50 km), but leaks to all fiberpositions after the PZT.

FIG. 3(B) shows amplitude vs distance along the 110 Hz line. The longtail after the PZT is fictitious, and is due to the vibration-inducedphase modulation terms in Eq. (9).

We note that the deleterious effect of multiplicative phase noiseinteracting with convolution by a linear impulse response is analogousto the phenomenon of equalization-enhanced phase noise (EEPN) previouslyobserved in telecommunications. In EEPN, the multiplicative phase noiseis that of the local oscillator laser, while the linear operator is theinverse chromatic dispersion (CD) of the fiber channel. It is known thatthe longer the duration of the CD, the more severe the impact of EEPN.

In Eq. (9) for phase distortion in TGD-OFDR, the variable to be detectedis g(t′) while the multiplicative phase noise is over x(t).Nevertheless, the same reasoning applies that the longer the duration ofx(t), the worse the phase distortion. This appears to place a limit onthe longest usable chirp duration T_(c)—vibration-induced phasedistortion favors the use of shorter chirp durations.

Reducing the impact of spatial leakage in DAS caused byvibration-induced phase modulation on long chirped pulses using amultiband digitally fragmented signal processing architecture. Bytruncating the transmitted chirped pulse into a series of shorter pulsesand processing them as distinct frequency channels, spatial leakage isreduced at the expense of reduced spatial resolution. However, we alsopropose that spatial resolution can be restored by chirping faster andusing a wider bandwidth receiver.

One particularly distinguishing aspect of systems, methods, andstructures according to aspects of the present disclosure includes ourinnovative digital signal processing architecture, where instead ofprocessing a transmitted chirped pulse as a single sequence, we use aparallel fragmented multiband architecture, where each tributarycorrelates the received signal with a truncated chirped pulse to obtainthe Rayleigh impulse response over its frequency band. Advantageously,by reducing the duration of the chirp processed by each tributary,spatial leakage is reduced at all the tributaries, thus even aftercombining all the interferometric products from all tributaries using arotated vector sum, the resultant signal is much less impacted byspatial leakage than by using a conventional, prior art TGD-OFDR method.

Of further advantage, our DSP architecture is also quite flexible, asthe number of fragmented tributaries to use at the receiver isindependent of the chirped pulse generator—i.e., the generator canalways transmit the same signal, it is up to the receiver how to processthe Rayleigh backscatter output to trade-off between good spatialresolution and low spatial leakage.

To mitigate against vibration-induced phase distortion on long chirpedpulses, the multiband digitally fragmented OFDR (MB-DF-OFDR) we proposedwill employ a digital signal processing architecture which partitionsthe chirped sequence x(t) into a concatenation of N_(b) shorter chirpsequences x_(b)(t), where:

$\begin{matrix}{{{x_{b}(t)} = {\sqrt{P}{\exp\left( {j\; 2\;{\pi\alpha}\frac{t^{2}}{2}} \right)}{{rect}\left( \frac{t - \tau_{b}}{T_{c}/N_{b}} \right)}}},{{{for}\mspace{14mu} b} = 1},\ldots\mspace{14mu},{N_{b}.}} & (10)\end{matrix}$

FIG. 4(A) and FIG. 4(B) are schematic illustrations showing thepartitioning of a long chirp sequence of duration T_(c) and bandwidthαT_(c) into N_(b) shorter chirp sequences, each of duration αT_(c)/N_(b)and duration T_(c)/N_(b) wherein FIG. 4(A) shows a time-domainrepresentation of a real part of x(t)=√{square root over (P)}exp(j2πα(t²/2)) for −T_(c)/2≤t<+T_(c)/2, and FIG. 4(B) shows aninstantaneous frequency of x(t), i.e., f(t)=αt for −T_(c)/2≤t<+T_(c)/2.

With respect to this figure, we note that each x_(b)(t) has durationT_(c)/N_(b) and is centered around delayτ_(b)=−T_(c)/2+(2b−1)(T_(c)/2N_(b)), and occupies frequency band

${{{- \frac{\alpha T_{c}}{2}} + {\left( {b - 1} \right)\frac{\alpha T_{c}}{N_{b}}}} \leq f_{b} \leq {{- \frac{\alpha T_{c}}{2}} + {b\frac{\alpha T_{c}}{N_{b}}}}},$

with f _(b)=ατ_(b) being the center of each band. The x_(b)(t) are alsomerely frequency-shifted and delayed copies of the same truncatedchirped pulse:

$\begin{matrix}{{x_{tr}(t)} = {\sqrt{P}{\exp\left( {j\; 2\;{\pi\alpha}\frac{t^{2}}{2}} \right)}{{rect}\left( \frac{t}{T_{c}/N_{b}} \right)}}} & (11) \\{{x_{b}(t)} = {{x_{tr}\left( {t - \tau_{b}} \right)}{\exp\left( {j\left( {{2\pi f_{b}t} + \theta_{b}} \right)} \right)}}} & (12)\end{matrix}$

Thus, it is possible to recover the Rayleigh impulse responseĝ_(b)(t)=[ĝ_(b,x)(t) ĝ_(b,y)(t)]^(T) for each frequency band f_(b) byfirst frequency shifting the received signal y(t) by −f_(b), thencorrelating with x_(tr)(t), followed by undoing the delay τ_(b).

Interferometric products between different polarization combinations (k,l)∈{x, y} of ĝ_(b) (t) are then computed at a gauge length of Δt_(g):

ζ_(b,kl)(t)=ĝ _(b,k)(t+Δt _(g))ĝ _(b,l)*(t)  (13)

These 4N_(b) interferometric product terms ζ_(b,kl)(t) can then beoptimally combined using a rotated vector sum to obtain ζ(t). Theunwrapped angle ∠ζ(t) is proportional to the cumulative strain betweenfiber positions z=(v_(g)/2)t and z+Δz_(g)=(v_(g)/2)(t+Δt_(g)).

Preserving Spatial Resolution

A drawback of partitioning x(t) into N_(b) shorter chirp sequences isthat each ĝ_(b)(t) will have bandwidth αT_(c)/N_(b)=1/N_(b)T, thus thespatial resolution of the resulting DAS is likewise reduced by a factorof N_(b) from the original (c/2n_(eff))T to (c/2n_(eff))N_(b)T.Depending on the application, this loss of spatial resolution may or maynot be desirable.

FIG. 5(A) and FIG. 5(B) are plots showing instantaneous frequencyprofile f(t) for: FIG. 5(A) TGD-OFDR frame; and FIG. 5(B) MB-DF-OFDRframe according to aspects of the present disclosure.

One way to retain the original spatial resolution is to increase thechirp rate by factor N_(b), resulting in the interrogation signal havingthe instantaneous frequency profile shown in FIG. 5(B). For convenienceof illustration, the origin of the time and frequency axes are shownshifted. The duration of the useful signal T_(c) is less than the frameperiod T_(f). To make the transmitted signal have constant envelope,therefore avoiding issues with amplifier gain transients, the rest ofthe frame is filled with out-of-band chirp, resulting in thetransmission of the following signal over each frame:

x(t)=√{square root over (P)}exp(j2π∫₀ ^(t) f(t′)dt′), for 0≤t<T_(f).  (14)

Since for T_(c)≤t<T_(f) in each frame, the instantaneous frequency f(t)is outside the bandwidth of the receiver, the out-of-band chirp does notimpact signal processing on the received signal. By chirping at anincreased rate of N_(b)α, the bandwidth covered by the truncated chirpedpulse x_(tr)(t) is restored to αT_(c)=1/T, hence spatial resolution isrestored to (c/2n_(eff))T. Furthermore, as the duration of x_(tr)(t) isT_(c)/N_(b), while the noise associated withx_(tr)*(t)*(y(t)exp(−j2πf_(b)t)) covers a bandwidth of 1/T, the SNR ofeach channel estimate ĝ_(b)(t) is 1/N_(b) times that of conventionalTGD-OFDR. After combining interferometric products from N_(b)tributaries, each with independent noises, the rotated sum vector ζ(t)will have the same SNR as conventional TGD-OFDR.

One drawback with the MB-DF-OFDR approach is that the coherent receiveroptics and ADCs needs to have sufficient bandwidth to have N_(b) thebandwidth to recover all N_(b) bands. There are also N_(b) tributariesto process, which increases DSP complexity. However, the increase in DSPcomplexity is less than linear since each x_(b)*(t) has shorterduration, and the downstream processing after obtaining ζ(t) is the sameas conventional TGD-OFDR.

As noted previously, our multiband DF-OFDR scheme uses the same physicalhardware as conventional TGD-OFDR and is shown in FIG. 1. Alow-linewidth continuous-wave (CW) laser is modulated with x(t) usingany standard method such as an arbitrary waveform generator (AWG)driving a Mach-Zehnder I/Q Modulator. The modulated signal is amplifiedto the correct power level and is launched into the FUT through acirculator. The Rayleigh backscatter is received on the third port ofthe circulator, which is amplified and filtered, before coherentdetection using the same CW laser which generated the outboundinterrogation signal as the local oscillator (LO). We assume a standardcoherent receiver front-end comprising a dual-polarization 90° opticalhybrid followed by balanced photodetectors (BPD), followed byanti-aliasing filtering to reject out-of-band chirp, followed bysampling and digitization by analog-to-digital converters (ADC). The ADCsampling rate T_(adc) should be sufficient to recover all N_(b)frequency bands in FIG. 5(A) without aliasing.

FIG. 6 shows a schematic diagram of an illustrative DSP architecture forMB-DF-OFDR according to aspects of the present disclosure. Withreference to that figure, we note that the digitized waveformy[n′]≙y(n′T_(adc)) recovered from the coherent receiver is processed inN_(b) parallel tributaries.

In tributary b, the received signal is first frequency downshifted by f_(b) followed by correlation with x_(tr)*[n′]≙x_(tr)*(n′T_(adc)) torecover the estimated ĝ_(b)[n′]−the Rayleigh impulse response forfrequency band f_(b). As ĝ_(b)[n′] only has bandwidth 1/N_(b)T, it isdownsampled to a lower rate of 1/T_(s), followed by timing realignmentby −n_(b)=−τ_(b)/T_(s) samples for each subband.

As the interrogator transmits the chirped sequence Σ_(m=−∞)^(+∞)x(t−mT_(f)) at a frame rate of T_(f)=N_(f)T_(s), the correlationreceiver output is periodic—i.e.,

${{\hat{g}}_{b}\left\lbrack {n + {mN}_{f}} \right\rbrack} \approx {\frac{v_{g}}{2}{h_{b}\left( {\frac{v_{g}}{2}nT_{s}} \right)}}$

is an estimator of the Rayleigh impulse response for frequency bandf_(b) at fiber position

$\frac{v_{g}}{2}nT_{s}$

during the transmission of the m-th frame. Interferometric products at apre-determined gauge length of Δz_(g)=(v_(g)/2)ΔnT_(s) are then computedfor the four combinations of polarizations (k, l)∈{x, y}:

ζ_(b,kl)[n]=ĝ _(b,k)[n+Δn]ĝ _(b,l)*[n].  (15)

The 4N_(b) time-aligned interferometric products are combined into arotated sum vector ζ[n]. One method to accomplish this is to firstparallelize ζ_(b,kl)[n]:

ζ_(b,kl) ^(p)[n,m]

ζ_(b,kl)[n+mN _(f)]  (16)

where n and m are the distance index and frame index, respectively. Ateach distance index n, the strongest interferometric product isselected:

$\begin{matrix}{\left( {b_{n},k_{n},l_{n}} \right) = {\max\limits_{b,k,l}\left\{ {\sum\limits_{m}{{\zeta_{b,{kl}}^{p}\left\lbrack {n,m} \right\rbrack}}^{2}} \right\}}} & (17)\end{matrix}$

The angle of all the other interferometric products relative to ζ_(b)_(n) _(,k) _(n) _(l) _(n) ^(p) are computed via an inner product,followed by a rotated vector sum operation to obtain ζ[n,m]:

$\begin{matrix}{\phi_{b,{kl},n} = {\angle\left( {\sum\limits_{m}{{\zeta_{b,{kl}}^{p}\left\lbrack {n,m} \right\rbrack}\left( {\zeta_{b_{n},{k_{n}l_{n}}}^{p}\left\lbrack {n,m} \right\rbrack} \right)^{*}}} \right)}} & (18) \\{{\zeta\left\lbrack {n,m} \right\rbrack} = {\underset{b = 1}{\sum\limits^{N_{b}}}{\sum\limits_{{({k,l})} \in {\{{x,y}\}}}{{\zeta_{b,{kl}}^{p}\left\lbrack {n,m} \right\rbrack}e^{{- j}\phi_{b,{kl},n}}}}}} & (19)\end{matrix}$

The unwrapped phase over index m of ζ[n, m] is the cumulativetime-varying longitudinal strain between fiber positions (v₉/2)nT_(s)and (v_(g)/2)(n+Δn)T_(s), at the time that the m-th frame wastransmitted. Further processing of ζ[n, m] may include taking the fastFourier transform over the time index m to reveal the frequency contentof the vibration at every fiber position. A neural network operating onζ[n, m] may also be used to classify the vibration event at every fiberposition.

FIG. 7(A) and FIG. 7(B) are plots showing DAS output obtained in afive-band MP-DF-OFDR experiment, showing improvement over TGD-OFDRwherein: FIG. 7(A) is of measured vibration spectrum versus distance;and FIG. 7(B) is of vibration power vs distance at 110 Hz, according toaspects of the present disclosure.

To illustrate the superior performance of the multiband DF-OFDR(MB-DF-OFDR) method, FIG. 7(A) and FIG. 7(B) show the same experiment asthat of FIG. 3(A) and FIG. 3(B), using a N_(b)=5 band implementation ofMB-DF-OFDR. The truncated chirped pulse x_(tr)(t) has durationT_(c)/N_(b)=10 μs and sweeps over a bandwidth of 1/N_(b)T=10 MHz.

The total bandwidth of x(t) is thus 50 MHz, compared to 10 MHz forconventional TGD-OFDR in FIG. 3(A) and FIG. 3(B). It is observed thatspatial leakage has been drastically reduced, as evidenced by the lackof a tail after the PZT at 50 km. Defining signal-to-interference ratio(SINR) to be the power difference between the peak at 50 km versus theaverage power after 50 km in FIG. 7(A) and FIG. 7(B), MB-DF-OFDRachieved an SINR of 34 dB, compared with 18 dB for conventionalTGD-OFDR.

At this point, while we have presented this disclosure using somespecific examples, those skilled in the art will recognize that ourteachings are not so limited. Accordingly, this disclosure should beonly limited by the scope of the claims attached hereto.

1. A distributed acoustic sensing (DTS) system comprising: a length ofoptical sensing fiber under test (FUT); and an optical pulse generatoroptically coupled to the FUT, said optical pulse generator configured togenerate and inject into the FUT chirped optical pulses of selectableduration and bandwidth at a frame rate limited by a round-trippropagation time of the pulses in the FUT; and a coherent receiveroptically coupled to the FUT, said coherent receiver configured todetect Rayleigh backscatter signal(s) from the FUT produced in the FUTin response to the injected chirped pulses injected therein.
 2. Thesystem of claim 1 further comprising a processor configured to determineacoustic vibrations affecting the FUT from the received Rayleighbackscatter signal(s).
 3. The system of claim 2 wherein the receiverincludes an optical hybrid, followed by balanced photodetectors, one ormore bandpass filters and one or more analog to digital converters. 4.The system of claim 3 further comprising a plurality of correlationreceivers, wherein the plurality of correlation receivers receives asinput, an output of the coherent receiver that is generated by thecoherent receiver in response to the Rayleigh backscatter signal(s). 5.The system of claim 4 wherein the number of correlation receiverscomprising the plurality of correlation receivers is selectable and notdependent on the chirped signal produced by the optical pulse generator.6. The system of claim 5 wherein the received Rayleigh backscattersignal(s) comprise a plurality of subbands and each individual onecorrelation receiver of the plurality of correlation receivers processesa different subband of the received Rayleigh backscatter signal(s). 7.The system of claim 1 wherein the processor is configured to perform aparallel fragmented multiband process instead of processing chirpedpulses as a single sequence such that each tributary correlates receivedsignals with a truncated chirped pulse to obtain a Rayleigh impulseresponse over its frequency band.
 8. The system of claim 7 wherein anumber of fragmented tributaries used is independent of the chirpedpulses generated such that the generator can always generate/transmitthe same signal.
 9. The system of claim 8 wherein the generator uses anarbitrary waveform generator to produce an electrical chirped signalwhich in turn drives a Mach-Zehnder I/Q modulator.